LMFDB - Embedded newform 900.3.p.f.101.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(101,900)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("900.101");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.12
Character	$\chi$	$=$	900.101
Dual form			900.3.p.f.401.12

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.88925 - 0.807601i) q^{3} +(6.19003 - 10.7214i) q^{7} +(7.69556 - 4.66673i) q^{9} +O(q^{10})$	\(q+(2.88925 - 0.807601i) q^{3} +(6.19003 - 10.7214i) q^{7} +(7.69556 - 4.66673i) q^{9} +(-4.00882 - 2.31449i) q^{11} +(0.631764 + 1.09425i) q^{13} -22.9122i q^{17} -32.8729 q^{19} +(9.22592 - 35.9760i) q^{21} +(0.690324 - 0.398559i) q^{23} +(18.4656 - 19.6983i) q^{27} +(34.3302 + 19.8206i) q^{29} +(-0.730215 - 1.26477i) q^{31} +(-13.4517 - 3.44963i) q^{33} -44.9884 q^{37} +(2.70904 + 2.65134i) q^{39} +(-33.8915 + 19.5673i) q^{41} +(-18.1908 + 31.5074i) q^{43} +(52.8629 + 30.5204i) q^{47} +(-52.1330 - 90.2970i) q^{49} +(-18.5039 - 66.1992i) q^{51} -13.9872i q^{53} +(-94.9780 + 26.5482i) q^{57} +(50.2415 - 29.0069i) q^{59} +(27.5253 - 47.6752i) q^{61} +(-2.39828 - 111.395i) q^{63} +(33.4960 + 58.0167i) q^{67} +(1.67264 - 1.70904i) q^{69} -70.6560i q^{71} +23.1498 q^{73} +(-49.6294 + 28.6536i) q^{77} +(-14.5725 + 25.2404i) q^{79} +(37.4434 - 71.8261i) q^{81} +(112.958 + 65.2165i) q^{83} +(115.196 + 29.5415i) q^{87} -48.0873i q^{89} +15.6425 q^{91} +(-3.13120 - 3.06452i) q^{93} +(9.68803 - 16.7802i) q^{97} +(-41.6512 + 0.896733i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{9}+O(q^{10}) $ 24 * q - 2 * q^9	$ 24 q - 2 q^{9} - 18 q^{11} - 26 q^{21} - 36 q^{29} + 30 q^{31} - 6 q^{39} - 36 q^{41} - 108 q^{49} + 124 q^{51} + 306 q^{59} + 48 q^{61} + 268 q^{69} - 114 q^{79} - 14 q^{81} - 84 q^{91} - 418 q^{99}+O(q^{100}) $ 24 * q - 2 * q^9 - 18 * q^11 - 26 * q^21 - 36 * q^29 + 30 * q^31 - 6 * q^39 - 36 * q^41 - 108 * q^49 + 124 * q^51 + 306 * q^59 + 48 * q^61 + 268 * q^69 - 114 * q^79 - 14 * q^81 - 84 * q^91 - 418 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	2.88925	−	0.807601i	0.963084	−	0.269200i
$3$	2.88925	−	0.807601i	0.963084	−	0.269200i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	6.19003	−	10.7214i	0.884290	−	1.53164i	0.0377652	−	0.999287i	$-0.487976\pi$
$7$	6.19003	−	10.7214i	0.884290	−	1.53164i	0.846525	−	0.532349i	$-0.178691\pi$
$8$		0			0
$9$	7.69556	−	4.66673i	0.855062	−	0.518525i
$10$		0			0
$11$	−4.00882	−	2.31449i	−0.364438	−	0.210408i	0.306588	−	0.951842i	$-0.400813\pi$
$11$	−4.00882	−	2.31449i	−0.364438	−	0.210408i	−0.671026	+	0.741434i	$0.734146\pi$
$12$		0			0
$13$	0.631764	+	1.09425i	0.0485972	+	0.0841728i	0.889301	−	0.457323i	$-0.151192\pi$
$13$	0.631764	+	1.09425i	0.0485972	+	0.0841728i	−0.840704	+	0.541496i	$0.817858\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	22.9122i		−	1.34778i	−0.738833	−	0.673889i	$-0.764623\pi$
$17$		−	22.9122i		−	1.34778i	0.738833	−	0.673889i	$-0.235377\pi$
$18$		0			0
$19$	−32.8729			−1.73015			−0.865075	−	0.501642i	$-0.832730\pi$
$19$	−32.8729			−1.73015			−0.865075	+	0.501642i	$0.832730\pi$
$20$		0			0
$21$	9.22592	−	35.9760i	0.439329	−	1.71315i
$22$		0			0
$23$	0.690324	−	0.398559i	0.0300141	−	0.0173286i	−0.484918	−	0.874560i	$-0.661151\pi$
$23$	0.690324	−	0.398559i	0.0300141	−	0.0173286i	0.514932	+	0.857231i	$0.327817\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	18.4656	−	19.6983i	0.683910	−	0.729566i
$28$		0			0
$29$	34.3302	+	19.8206i	1.18380	+	0.683468i	0.956891	−	0.290448i	$-0.0938042\pi$
$29$	34.3302	+	19.8206i	1.18380	+	0.683468i	0.226910	+	0.973916i	$0.427138\pi$
$30$		0			0
$31$	−0.730215	−	1.26477i	−0.0235553	−	0.0407990i	0.854007	−	0.520261i	$-0.174165\pi$
$31$	−0.730215	−	1.26477i	−0.0235553	−	0.0407990i	−0.877563	+	0.479462i	$0.840832\pi$
$32$		0			0
$33$	−13.4517	−	3.44963i	−0.407627	−	0.104534i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−44.9884			−1.21590			−0.607952	−	0.793974i	$-0.708009\pi$
$37$	−44.9884			−1.21590			−0.607952	+	0.793974i	$0.708009\pi$
$38$		0			0
$39$	2.70904	+	2.65134i	0.0694626	+	0.0679831i
$40$		0			0
$41$	−33.8915	+	19.5673i	−0.826623	+	0.477251i	−0.852695	−	0.522409i	$-0.825033\pi$
$41$	−33.8915	+	19.5673i	−0.826623	+	0.477251i	0.0260720	+	0.999660i	$0.491700\pi$
$42$		0			0
$43$	−18.1908	+	31.5074i	−0.423043	+	0.732731i	−0.996235	−	0.0866892i	$-0.972371\pi$
$43$	−18.1908	+	31.5074i	−0.423043	+	0.732731i	0.573193	+	0.819421i	$0.305705\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	52.8629	+	30.5204i	1.12474	+	0.649370i	0.942607	−	0.333904i	$-0.108366\pi$
$47$	52.8629	+	30.5204i	1.12474	+	0.649370i	0.182134	+	0.983274i	$0.441699\pi$
$48$		0			0
$49$	−52.1330	−	90.2970i	−1.06394	−	1.84280i
$50$		0			0
$51$	−18.5039	−	66.1992i	−0.362822	−	1.29802i
$52$		0			0
$53$		−	13.9872i		−	0.263909i	−0.991256	−	0.131954i	$-0.957875\pi$
$53$		−	13.9872i		−	0.263909i	0.991256	−	0.131954i	$-0.0421252\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−94.9780	+	26.5482i	−1.66628	+	0.465757i
$58$		0			0
$59$	50.2415	−	29.0069i	0.851550	−	0.491643i	−0.00962347	−	0.999954i	$-0.503063\pi$
$59$	50.2415	−	29.0069i	0.851550	−	0.491643i	0.861174	+	0.508311i	$0.169730\pi$
$60$		0			0
$61$	27.5253	−	47.6752i	0.451234	−	0.781561i	−0.547229	−	0.836983i	$-0.684317\pi$
$61$	27.5253	−	47.6752i	0.451234	−	0.781561i	0.998463	+	0.0554222i	$0.0176505\pi$
$62$		0			0
$63$	−2.39828	−	111.395i	−0.0380680	−	1.76817i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	33.4960	+	58.0167i	0.499940	+	0.865921i	1.00000		6.94337e-5i	$-2.21014e-5\pi$
$67$	33.4960	+	58.0167i	0.499940	+	0.865921i	−0.500060	+	0.865991i	$0.666689\pi$
$68$		0			0
$69$	1.67264	−	1.70904i	0.0242412	−	0.0247687i
$70$		0			0
$71$		−	70.6560i		−	0.995156i	−0.867419	−	0.497578i	$-0.834223\pi$
$71$		−	70.6560i		−	0.995156i	0.867419	−	0.497578i	$-0.165777\pi$
$72$		0			0
$73$	23.1498			0.317121			0.158561	−	0.987349i	$-0.449315\pi$
$73$	23.1498			0.317121			0.158561	+	0.987349i	$0.449315\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−49.6294	+	28.6536i	−0.644538	+	0.372124i
$78$		0			0
$79$	−14.5725	+	25.2404i	−0.184462	+	0.319498i	−0.943395	−	0.331671i	$-0.892388\pi$
$79$	−14.5725	+	25.2404i	−0.184462	+	0.319498i	0.758933	+	0.651169i	$0.225721\pi$
$80$		0			0
$81$	37.4434	−	71.8261i	0.462264	−	0.886743i
$82$		0			0
$83$	112.958	+	65.2165i	1.36094	+	0.785741i	0.989749	−	0.142815i	$-0.0456154\pi$
$83$	112.958	+	65.2165i	1.36094	+	0.785741i	0.371193	+	0.928556i	$0.378949\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	115.196	+	29.5415i	1.32409	+	0.339558i
$88$		0			0
$89$		−	48.0873i		−	0.540307i	−0.962817	−	0.270153i	$-0.912926\pi$
$89$		−	48.0873i		−	0.540307i	0.962817	−	0.270153i	$-0.0870744\pi$
$90$		0			0
$91$	15.6425			0.171896
$92$		0			0
$93$	−3.13120	−	3.06452i	−0.0336689	−	0.0329518i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	9.68803	−	16.7802i	0.0998766	−	0.172991i	−0.811757	−	0.583996i	$-0.801489\pi$
$97$	9.68803	−	16.7802i	0.0998766	−	0.172991i	0.911633	+	0.411004i	$0.134822\pi$
$98$		0			0
$99$	−41.6512	+	0.896733i	−0.420719	+	0.00905791i
$100$		0			0
$101$	−112.152	−	64.7508i	−1.11041	−	0.641097i	−0.171476	−	0.985188i	$-0.554854\pi$
$101$	−112.152	−	64.7508i	−1.11041	−	0.641097i	−0.938936	+	0.344092i	$0.888187\pi$
$102$		0			0
$103$	−4.20123	−	7.27674i	−0.0407886	−	0.0706480i	0.844910	−	0.534908i	$-0.179654\pi$
$103$	−4.20123	−	7.27674i	−0.0407886	−	0.0706480i	−0.885699	+	0.464260i	$0.846320\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	61.1389i		−	0.571391i	−0.958320	−	0.285696i	$-0.907775\pi$
$107$		−	61.1389i		−	0.571391i	0.958320	−	0.285696i	$-0.0922246\pi$
$108$		0			0
$109$	161.771			1.48414			0.742068	−	0.670324i	$-0.233845\pi$
$109$	161.771			1.48414			0.742068	+	0.670324i	$0.233845\pi$
$110$		0			0
$111$	−129.983	+	36.3327i	−1.17102	+	0.327322i
$112$		0			0
$113$	29.6592	−	17.1238i	0.262471	−	0.151538i	−0.362990	−	0.931793i	$-0.618244\pi$
$113$	29.6592	−	17.1238i	0.262471	−	0.151538i	0.625461	+	0.780255i	$0.284911\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	9.96833	+	5.47258i	0.0851994	+	0.0467742i
$118$		0			0
$119$	−245.652	−	141.827i	−2.06430	−	1.19183i
$120$		0			0
$121$	−49.7862	−	86.2323i	−0.411457	−	0.712664i
$122$		0			0
$123$	−82.1187	+	83.9057i	−0.667632	+	0.682160i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−104.320			−0.821421			−0.410710	−	0.911766i	$-0.634719\pi$
$127$	−104.320			−0.821421			−0.410710	+	0.911766i	$0.634719\pi$
$128$		0			0
$129$	−27.1125	+	105.724i	−0.210174	+	0.819565i
$130$		0			0
$131$	190.209	−	109.817i	1.45198	−	0.838299i	0.453382	−	0.891316i	$-0.350217\pi$
$131$	190.209	−	109.817i	1.45198	−	0.838299i	0.998594	+	0.0530175i	$0.0168839\pi$
$132$		0			0
$133$	−203.484	+	352.445i	−1.52996	+	2.64996i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	164.090	+	94.7374i	1.19774	+	0.691514i	0.960050	−	0.279828i	$-0.0902776\pi$
$137$	164.090	+	94.7374i	1.19774	+	0.691514i	0.237687	+	0.971342i	$0.423611\pi$
$138$		0			0
$139$	110.020	+	190.560i	0.791511	+	1.37094i	0.925031	+	0.379892i	$0.124039\pi$
$139$	110.020	+	190.560i	0.791511	+	1.37094i	−0.133520	+	0.991046i	$0.542628\pi$
$140$		0			0
$141$	177.382	+	45.4890i	1.25803	+	0.322617i
$142$		0			0
$143$		−	5.84885i		−	0.0409010i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−223.549	−	218.788i	−1.52074	−	1.48835i
$148$		0			0
$149$	9.00402	−	5.19847i	0.0604297	−	0.0348891i	−0.469481	−	0.882943i	$-0.655559\pi$
$149$	9.00402	−	5.19847i	0.0604297	−	0.0348891i	0.529910	+	0.848054i	$0.322226\pi$
$150$		0			0
$151$	40.8811	−	70.8081i	0.270736	−	0.468928i	−0.698315	−	0.715791i	$-0.746066\pi$
$151$	40.8811	−	70.8081i	0.270736	−	0.468928i	0.969050	+	0.246863i	$0.0793998\pi$
$152$		0			0
$153$	−106.925	−	176.322i	−0.698856	−	1.15243i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	66.1558	+	114.585i	0.421375	+	0.729842i	0.996074	−	0.0885222i	$-0.0282144\pi$
$157$	66.1558	+	114.585i	0.421375	+	0.729842i	−0.574700	+	0.818364i	$0.694881\pi$
$158$		0			0
$159$	−11.2960	−	40.4124i	−0.0710443	−	0.254166i
$160$		0			0
$161$		−	9.86836i		−	0.0612942i
$162$		0			0
$163$	−81.7721			−0.501669			−0.250835	−	0.968030i	$-0.580705\pi$
$163$	−81.7721			−0.501669			−0.250835	+	0.968030i	$0.580705\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−23.9909	+	13.8512i	−0.143658	+	0.0829411i	−0.570106	−	0.821571i	$-0.693098\pi$
$167$	−23.9909	+	13.8512i	−0.143658	+	0.0829411i	0.426448	+	0.904512i	$0.359765\pi$
$168$		0			0
$169$	83.7017	−	144.976i	0.495277	−	0.857844i
$170$		0			0
$171$	−252.975	+	153.409i	−1.47939	+	0.897127i
$172$		0			0
$173$	241.288	+	139.308i	1.39473	+	0.805246i	0.993834	−	0.110878i	$-0.0353663\pi$
$173$	241.288	+	139.308i	1.39473	+	0.805246i	0.400894	+	0.916125i	$0.368700\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	121.734	−	124.383i	0.687764	−	0.702731i
$178$		0			0
$179$			175.928i			0.982839i	0.870923	+	0.491419i	$0.163522\pi$
$179$			175.928i			0.982839i	−0.870923	+	0.491419i	$0.836478\pi$
$180$		0			0
$181$	−180.887			−0.999377			−0.499689	−	0.866205i	$-0.666552\pi$
$181$	−180.887			−0.999377			−0.499689	+	0.866205i	$0.666552\pi$
$182$		0			0
$183$	41.0250	−	159.975i	0.224180	−	0.874181i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−53.0302	+	91.8509i	−0.283584	+	0.491181i
$188$		0			0
$189$	−96.8917	−	319.911i	−0.512655	−	1.69265i
$190$		0			0
$191$	120.178	+	69.3846i	0.629202	+	0.363270i	0.780443	−	0.625227i	$-0.214994\pi$
$191$	120.178	+	69.3846i	0.629202	+	0.363270i	−0.151241	+	0.988497i	$0.548327\pi$
$192$		0			0
$193$	−89.4876	−	154.997i	−0.463666	−	0.803093i	0.535474	−	0.844552i	$-0.320133\pi$
$193$	−89.4876	−	154.997i	−0.463666	−	0.803093i	−0.999140	+	0.0414582i	$0.986800\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	136.877i		−	0.694809i	−0.937715	−	0.347405i	$-0.887063\pi$
$197$		−	136.877i		−	0.694809i	0.937715	−	0.347405i	$-0.112937\pi$
$198$		0			0
$199$	−11.4634			−0.0576050			−0.0288025	−	0.999585i	$-0.509169\pi$
$199$	−11.4634			−0.0576050			−0.0288025	+	0.999585i	$0.509169\pi$
$200$		0			0
$201$	143.633	+	140.574i	0.714590	+	0.699371i
$202$		0			0
$203$	425.010	−	245.380i	2.09365	−	1.20877i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	3.45247	−	6.28869i	0.0166786	−	0.0303801i
$208$		0			0
$209$	131.781	+	76.0840i	0.630533	+	0.364038i
$210$		0			0
$211$	38.7228	+	67.0698i	0.183520	+	0.317867i	0.943077	−	0.332575i	$-0.107917\pi$
$211$	38.7228	+	67.0698i	0.183520	+	0.317867i	−0.759557	+	0.650441i	$0.774584\pi$
$212$		0			0
$213$	−57.0619	−	204.143i	−0.267896	−	0.958419i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−18.0802			−0.0833190
$218$		0			0
$219$	66.8857	−	18.6958i	0.305414	−	0.0853691i
$220$		0			0
$221$	25.0716	−	14.4751i	0.113446	−	0.0654982i
$222$		0			0
$223$	−72.1175	+	124.911i	−0.323397	+	0.560140i	−0.981187	−	0.193062i	$-0.938158\pi$
$223$	−72.1175	+	124.911i	−0.323397	+	0.560140i	0.657790	+	0.753202i	$0.271492\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−42.5248	−	24.5517i	−0.187334	−	0.108157i	0.403400	−	0.915024i	$-0.367828\pi$
$227$	−42.5248	−	24.5517i	−0.187334	−	0.108157i	−0.590734	+	0.806867i	$0.701162\pi$
$228$		0			0
$229$	−50.4902	−	87.4515i	−0.220481	−	0.381884i	0.734473	−	0.678638i	$-0.237429\pi$
$229$	−50.4902	−	87.4515i	−0.220481	−	0.381884i	−0.954954	+	0.296753i	$0.904096\pi$
$230$		0			0
$231$	−120.251	+	122.868i	−0.520568	+	0.531897i
$232$		0			0
$233$		−	120.466i		−	0.517021i	−0.966009	−	0.258510i	$-0.916768\pi$
$233$		−	120.466i		−	0.517021i	0.966009	−	0.258510i	$-0.0832316\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−21.7196	+	84.6946i	−0.0916438	+	0.357361i
$238$		0			0
$239$	−157.093	+	90.6979i	−0.657294	+	0.379489i	−0.791245	−	0.611499i	$-0.790567\pi$
$239$	−157.093	+	90.6979i	−0.657294	+	0.379489i	0.133951	+	0.990988i	$0.457234\pi$
$240$		0			0
$241$	−81.1538	+	140.562i	−0.336738	+	0.583247i	−0.983817	−	0.179176i	$-0.942657\pi$
$241$	−81.1538	+	140.562i	−0.336738	+	0.583247i	0.647079	+	0.762423i	$0.275990\pi$
$242$		0			0
$243$	50.1765	−	237.763i	0.206488	−	0.978449i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−20.7679	−	35.9710i	−0.0840805	−	0.145632i
$248$		0			0
$249$	379.034	+	97.2017i	1.52222	+	0.390368i
$250$		0			0
$251$			445.457i			1.77473i	0.461069	+	0.887364i	$0.347466\pi$
$251$			445.457i			1.77473i	−0.461069	+	0.887364i	$0.652534\pi$
$252$		0			0
$253$	−3.68984			−0.0145844
$254$		0			0
$255$		0			0
$256$		0			0
$257$	214.270	−	123.709i	0.833734	−	0.481357i	−0.0213954	−	0.999771i	$-0.506811\pi$
$257$	214.270	−	123.709i	0.833734	−	0.481357i	0.855129	+	0.518414i	$0.173478\pi$
$258$		0			0
$259$	−278.480	+	482.341i	−1.07521	+	1.86232i
$260$		0			0
$261$	356.688	−	7.67933i	1.36662	−	0.0294227i
$262$		0			0
$263$	74.4992	+	43.0121i	0.283267	+	0.163544i	0.634901	−	0.772593i	$-0.281041\pi$
$263$	74.4992	+	43.0121i	0.283267	+	0.163544i	−0.351635	+	0.936137i	$0.614374\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−38.8353	−	138.936i	−0.145451	−	0.520361i
$268$		0			0
$269$			368.618i			1.37033i	0.728389	+	0.685164i	$0.240269\pi$
$269$			368.618i			1.37033i	−0.728389	+	0.685164i	$0.759731\pi$
$270$		0			0
$271$	−130.740			−0.482434			−0.241217	−	0.970471i	$-0.577546\pi$
$271$	−130.740			−0.482434			−0.241217	+	0.970471i	$0.577546\pi$
$272$		0			0
$273$	45.1953	−	12.6329i	0.165550	−	0.0462745i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	108.635	−	188.162i	0.392185	−	0.679284i	−0.600553	−	0.799585i	$-0.705053\pi$
$277$	108.635	−	188.162i	0.392185	−	0.679284i	0.992737	+	0.120301i	$0.0383860\pi$
$278$		0			0
$279$	−11.5217	−	6.32540i	−0.0412966	−	0.0226717i
$280$		0			0
$281$	149.240	+	86.1636i	0.531102	+	0.306632i	0.741465	−	0.670991i	$-0.234131\pi$
$281$	149.240	+	86.1636i	0.531102	+	0.306632i	−0.210363	+	0.977623i	$0.567465\pi$
$282$		0			0
$283$	218.079	+	377.723i	0.770596	+	1.33471i	0.937237	+	0.348694i	$0.113375\pi$
$283$	218.079	+	377.723i	0.770596	+	1.33471i	−0.166640	+	0.986018i	$0.553292\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			484.489i			1.68811i
$288$		0			0
$289$	−235.970			−0.816504
$290$		0			0
$291$	14.4395	−	56.3062i	0.0496203	−	0.193492i
$292$		0			0
$293$	−25.1499	+	14.5203i	−0.0858359	+	0.0495574i	−0.542304	−	0.840183i	$-0.682448\pi$
$293$	−25.1499	+	14.5203i	−0.0858359	+	0.0495574i	0.456468	+	0.889740i	$0.349114\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−119.617	+	36.2284i	−0.402750	+	0.121981i
$298$		0			0
$299$	0.872243	+	0.503590i	0.00291720	+	0.00168425i
$300$		0			0
$301$	225.204	+	390.064i	0.748185	+	1.29589i
$302$		0			0
$303$	−376.327	−	96.5076i	−1.24200	−	0.318507i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−306.163			−0.997273			−0.498637	−	0.866811i	$-0.666166\pi$
$307$	−306.163			−0.997273			−0.498637	+	0.866811i	$0.666166\pi$
$308$		0			0
$309$	−18.0151	−	17.6314i	−0.0583013	−	0.0570596i
$310$		0			0
$311$	−344.003	+	198.610i	−1.10612	+	0.638618i	−0.937821	−	0.347118i	$-0.887160\pi$
$311$	−344.003	+	198.610i	−1.10612	+	0.638618i	−0.168298	+	0.985736i	$0.553827\pi$
$312$		0			0
$313$	−195.881	+	339.276i	−0.625818	+	1.08395i	0.362564	+	0.931959i	$0.381901\pi$
$313$	−195.881	+	339.276i	−0.625818	+	1.08395i	−0.988382	+	0.151990i	$0.951432\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−140.112	−	80.8940i	−0.441995	−	0.255186i	0.262448	−	0.964946i	$-0.415470\pi$
$317$	−140.112	−	80.8940i	−0.441995	−	0.255186i	−0.704444	+	0.709760i	$0.748803\pi$
$318$		0			0
$319$	−91.7491	−	158.914i	−0.287615	−	0.498164i
$320$		0			0
$321$	−49.3758	−	176.646i	−0.153819	−	0.550298i
$322$		0			0
$323$			753.190i			2.33186i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	467.397	−	130.646i	1.42935	−	0.399530i
$328$		0			0
$329$	654.446	−	377.844i	1.98920	−	1.14846i
$330$		0			0
$331$	−118.594	+	205.411i	−0.358291	+	0.620578i	−0.987675	−	0.156516i	$-0.949974\pi$
$331$	−118.594	+	205.411i	−0.358291	+	0.620578i	0.629385	+	0.777094i	$0.283307\pi$
$332$		0			0
$333$	−346.211	+	209.949i	−1.03967	+	0.630476i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	211.024	+	365.505i	0.626185	+	1.08458i	0.988310	+	0.152455i	$0.0487179\pi$
$337$	211.024	+	365.505i	0.626185	+	1.08458i	−0.362125	+	0.932129i	$0.617949\pi$
$338$		0			0
$339$	71.8638	−	73.4276i	0.211988	−	0.216601i
$340$		0			0
$341$			6.76031i			0.0198250i
$342$		0			0
$343$	−684.196			−1.99474
$344$		0			0
$345$		0			0
$346$		0			0
$347$	478.474	−	276.247i	1.37889	−	0.796102i	0.386863	−	0.922137i	$-0.373559\pi$
$347$	478.474	−	276.247i	1.37889	−	0.796102i	0.992026	+	0.126036i	$0.0402253\pi$
$348$		0			0
$349$	198.589	−	343.966i	0.569022	−	0.985575i	−0.427641	−	0.903949i	$-0.640655\pi$
$349$	198.589	−	343.966i	0.569022	−	0.985575i	0.996663	−	0.0816263i	$-0.0260114\pi$
$350$		0			0
$351$	33.2207	+	7.76123i	0.0946458	+	0.0221118i
$352$		0			0
$353$	267.320	+	154.337i	0.757281	+	0.437216i	0.828319	−	0.560257i	$-0.189298\pi$
$353$	267.320	+	154.337i	0.757281	+	0.437216i	−0.0710376	+	0.997474i	$0.522631\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−824.291	−	211.386i	−2.30894	−	0.592118i
$358$		0			0
$359$			278.225i			0.775000i	0.921870	+	0.387500i	$0.126661\pi$
$359$			278.225i			0.775000i	−0.921870	+	0.387500i	$0.873339\pi$
$360$		0			0
$361$	719.626			1.99342
$362$		0			0
$363$	−213.486	−	208.940i	−0.588117	−	0.575591i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−304.122	+	526.754i	−0.828669	+	1.43530i	0.0704128	+	0.997518i	$0.477568\pi$
$367$	−304.122	+	526.754i	−0.828669	+	1.43530i	−0.899082	+	0.437780i	$0.855765\pi$
$368$		0			0
$369$	−169.499	+	308.744i	−0.459348	+	0.836704i
$370$		0			0
$371$	−149.963	−	86.5810i	−0.404212	−	0.233372i
$372$		0			0
$373$	179.439	+	310.798i	0.481070	+	0.833238i	0.999764	−	0.0217222i	$-0.00691493\pi$
$373$	179.439	+	310.798i	0.481070	+	0.833238i	−0.518694	+	0.854960i	$0.673582\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			50.0877i			0.132859i
$378$		0			0
$379$	−353.208			−0.931948			−0.465974	−	0.884798i	$-0.654296\pi$
$379$	−353.208			−0.931948			−0.465974	+	0.884798i	$0.654296\pi$
$380$		0			0
$381$	−301.408	+	84.2493i	−0.791097	+	0.221127i
$382$		0			0
$383$	235.029	−	135.694i	0.613653	−	0.354293i	−0.160741	−	0.986997i	$-0.551388\pi$
$383$	235.029	−	135.694i	0.613653	−	0.354293i	0.774394	+	0.632704i	$0.218055\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	7.04790	+	327.359i	0.0182116	+	0.845889i
$388$		0			0
$389$	−227.502	−	131.349i	−0.584839	−	0.337657i	0.178215	−	0.983992i	$-0.442968\pi$
$389$	−227.502	−	131.349i	−0.584839	−	0.337657i	−0.763054	+	0.646334i	$0.776301\pi$
$390$		0			0
$391$	−9.13186	−	15.8169i	−0.0233552	−	0.0404523i
$392$		0			0
$393$	460.873	−	470.902i	1.17270	−	1.19822i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	53.4516			0.134639			0.0673194	−	0.997731i	$-0.478555\pi$
$397$	53.4516			0.134639			0.0673194	+	0.997731i	$0.478555\pi$
$398$		0			0
$399$	−303.282	+	1182.64i	−0.760106	+	2.96400i
$400$		0			0
$401$	−160.143	+	92.4584i	−0.399358	+	0.230570i	−0.686207	−	0.727406i	$-0.740726\pi$
$401$	−160.143	+	92.4584i	−0.399358	+	0.230570i	0.286849	+	0.957976i	$0.407392\pi$
$402$		0			0
$403$	0.922647	−	1.59807i	0.00228945	−	0.00396544i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	180.350	+	104.125i	0.443122	+	0.255836i
$408$		0			0
$409$	116.052	+	201.008i	0.283746	+	0.491463i	0.972304	−	0.233718i	$-0.0750893\pi$
$409$	116.052	+	201.008i	0.283746	+	0.491463i	−0.688558	+	0.725181i	$0.741756\pi$
$410$		0			0
$411$	550.607	+	141.201i	1.33968	+	0.343555i
$412$		0			0
$413$		−	718.215i		−	1.73902i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	471.772	+	461.725i	1.13135	+	1.10725i
$418$		0			0
$419$	336.098	−	194.046i	0.802143	−	0.463117i	−0.0420770	−	0.999114i	$-0.513397\pi$
$419$	336.098	−	194.046i	0.802143	−	0.463117i	0.844220	+	0.535997i	$0.180064\pi$
$420$		0			0
$421$	−77.0016	+	133.371i	−0.182902	+	0.316795i	−0.942867	−	0.333168i	$-0.891882\pi$
$421$	−77.0016	+	133.371i	−0.182902	+	0.316795i	0.759966	+	0.649963i	$0.225216\pi$
$422$		0			0
$423$	549.240	−	11.8249i	1.29844	−	0.0279548i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−340.765	−	590.222i	−0.798044	−	1.38225i
$428$		0			0
$429$	−4.72354	−	16.8988i	−0.0110106	−	0.0393912i
$430$		0			0
$431$			238.147i			0.552544i	0.961079	+	0.276272i	$0.0890991\pi$
$431$			238.147i			0.552544i	−0.961079	+	0.276272i	$0.910901\pi$
$432$		0			0
$433$	523.956			1.21006			0.605030	−	0.796203i	$-0.293161\pi$
$433$	523.956			1.21006			0.605030	+	0.796203i	$0.293161\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−22.6929	+	13.1018i	−0.0519289	+	0.0299812i
$438$		0			0
$439$	228.172	−	395.206i	0.519755	−	0.900242i	−0.479982	−	0.877279i	$-0.659357\pi$
$439$	228.172	−	395.206i	0.519755	−	0.900242i	0.999736	−	0.0229630i	$-0.00730999\pi$
$440$		0			0
$441$	−822.584	−	451.596i	−1.86527	−	1.02403i
$442$		0			0
$443$	−235.368	−	135.890i	−0.531305	−	0.306749i	0.210242	−	0.977649i	$-0.432575\pi$
$443$	−235.368	−	135.890i	−0.531305	−	0.306749i	−0.741548	+	0.670900i	$0.765908\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	21.8166	−	22.2914i	0.0488067	−	0.0498688i
$448$		0			0
$449$		−	386.192i		−	0.860116i	−0.902801	−	0.430058i	$-0.858493\pi$
$449$		−	386.192i		−	0.860116i	0.902801	−	0.430058i	$-0.141507\pi$
$450$		0			0
$451$	181.153			0.401671
$452$		0			0
$453$	60.9311	−	237.598i	0.134506	−	0.524499i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−2.24416	+	3.88700i	−0.00491063	+	0.00850546i	−0.868470	−	0.495741i	$-0.834896\pi$
$457$	−2.24416	+	3.88700i	−0.00491063	+	0.00850546i	0.863560	+	0.504247i	$0.168230\pi$
$458$		0			0
$459$	−451.331	−	423.087i	−0.983293	−	0.921759i
$460$		0			0
$461$	−283.502	−	163.680i	−0.614972	−	0.355054i	0.159937	−	0.987127i	$-0.448871\pi$
$461$	−283.502	−	163.680i	−0.614972	−	0.355054i	−0.774909	+	0.632073i	$0.782204\pi$
$462$		0			0
$463$	−106.071	−	183.720i	−0.229094	−	0.396803i	0.728446	−	0.685103i	$-0.240243\pi$
$463$	−106.071	−	183.720i	−0.229094	−	0.396803i	−0.957540	+	0.288301i	$0.906910\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			471.246i			1.00909i	0.863385	+	0.504546i	$0.168340\pi$
$467$			471.246i			1.00909i	−0.863385	+	0.504546i	$0.831660\pi$
$468$		0			0
$469$	829.364			1.76837
$470$		0			0
$471$	283.680	+	277.638i	0.602293	+	0.589465i
$472$		0			0
$473$	145.847	−	84.2051i	0.308346	−	0.178023i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−65.2742	−	107.639i	−0.136843	−	0.225658i
$478$		0			0
$479$	−762.164	−	440.035i	−1.59116	−	0.918654i	−0.993109	−	0.117193i	$-0.962610\pi$
$479$	−762.164	−	440.035i	−1.59116	−	0.918654i	−0.598047	−	0.801461i	$-0.704056\pi$
$480$		0			0
$481$	−28.4221	−	49.2285i	−0.0590895	−	0.102346i
$482$		0			0
$483$	−7.96970	−	28.5122i	−0.0165004	−	0.0590315i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	606.421			1.24522			0.622609	−	0.782533i	$-0.286073\pi$
$487$	606.421			1.24522			0.622609	+	0.782533i	$0.286073\pi$
$488$		0			0
$489$	−236.260	+	66.0392i	−0.483150	+	0.135050i
$490$		0			0
$491$	488.016	−	281.756i	0.993922	−	0.573841i	0.0874776	−	0.996166i	$-0.472119\pi$
$491$	488.016	−	281.756i	0.993922	−	0.573841i	0.906444	+	0.422325i	$0.138786\pi$
$492$		0			0
$493$	454.133	−	786.582i	0.921163	−	1.59550i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−757.535	−	437.363i	−1.52422	−	0.880006i
$498$		0			0
$499$	35.9407	+	62.2511i	0.0720254	+	0.124752i	0.899789	−	0.436326i	$-0.143720\pi$
$499$	35.9407	+	62.2511i	0.0720254	+	0.124752i	−0.827763	+	0.561077i	$0.810387\pi$
$500$		0			0
$501$	−58.1296	+	59.3946i	−0.116027	+	0.118552i
$502$		0			0
$503$			124.538i			0.247591i	0.992308	+	0.123795i	$0.0395067\pi$
$503$			124.538i			0.247591i	−0.992308	+	0.123795i	$0.960493\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	124.753	−	486.469i	0.246061	−	0.959505i
$508$		0			0
$509$	466.058	−	269.079i	0.915634	−	0.528642i	0.0333945	−	0.999442i	$-0.489368\pi$
$509$	466.058	−	269.079i	0.915634	−	0.528642i	0.882240	+	0.470801i	$0.156035\pi$
$510$		0			0
$511$	143.298	−	248.200i	0.280427	−	0.485714i
$512$		0			0
$513$	−607.016	+	647.539i	−1.18327	+	1.26226i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−141.278	−	244.701i	−0.273266	−	0.473310i
$518$		0			0
$519$	809.647	+	207.631i	1.56001	+	0.400059i
$520$		0			0
$521$		−	147.767i		−	0.283622i	−0.989894	−	0.141811i	$-0.954707\pi$
$521$		−	147.767i		−	0.283622i	0.989894	−	0.141811i	$-0.0452925\pi$
$522$		0			0
$523$	−701.166			−1.34066			−0.670331	−	0.742063i	$-0.733848\pi$
$523$	−701.166			−1.34066			−0.670331	+	0.742063i	$0.733848\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−28.9787	+	16.7308i	−0.0549880	+	0.0317473i
$528$		0			0
$529$	−264.182	+	457.577i	−0.499399	+	0.864985i
$530$		0			0
$531$	251.269	−	457.688i	0.473200	−	0.861935i
$532$		0			0
$533$	−42.8229	−	24.7238i	−0.0803431	−	0.0463861i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	142.080	+	508.301i	0.264580	+	0.946556i
$538$		0			0
$539$			482.646i			0.895446i
$540$		0			0
$541$	−573.411			−1.05991			−0.529955	−	0.848026i	$-0.677791\pi$
$541$	−573.411			−1.05991			−0.529955	+	0.848026i	$0.677791\pi$
$542$		0			0
$543$	−522.629	+	146.085i	−0.962484	+	0.269033i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−152.510	+	264.155i	−0.278812	+	0.482916i	−0.971090	−	0.238715i	$-0.923274\pi$
$547$	−152.510	+	264.155i	−0.278812	+	0.482916i	0.692278	+	0.721631i	$0.256607\pi$
$548$		0			0
$549$	−10.6645	−	495.341i	−0.0194253	−	0.902260i
$550$		0			0
$551$	−1128.53	−	651.559i	−2.04815	−	1.18250i
$552$		0			0
$553$	180.409	+	312.477i	0.326237	+	0.565058i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	686.875i		−	1.23317i	−0.787288	−	0.616585i	$-0.788516\pi$
$557$		−	686.875i		−	1.23317i	0.787288	−	0.616585i	$-0.211484\pi$
$558$		0			0
$559$	−45.9692			−0.0822348
$560$		0			0
$561$	−79.0386	+	308.208i	−0.140889	+	0.549390i
$562$		0			0
$563$	−402.756	+	232.531i	−0.715374	+	0.413021i	−0.813048	−	0.582197i	$-0.802193\pi$
$563$	−402.756	+	232.531i	−0.715374	+	0.413021i	0.0976736	+	0.995219i	$0.468860\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−538.305	−	846.053i	−0.949391	−	1.49216i
$568$		0			0
$569$	−954.086	−	550.842i	−1.67678	−	0.968088i	−0.963694	−	0.267009i	$-0.913965\pi$
$569$	−954.086	−	550.842i	−1.67678	−	0.968088i	−0.713084	−	0.701079i	$-0.752702\pi$
$570$		0			0
$571$	−381.027	−	659.958i	−0.667298	−	1.15579i	−0.978657	−	0.205501i	$-0.934118\pi$
$571$	−381.027	−	659.958i	−0.667298	−	1.15579i	0.311359	−	0.950292i	$-0.399216\pi$
$572$		0			0
$573$	403.259	+	103.414i	0.703767	+	0.180478i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	673.918			1.16797			0.583985	−	0.811765i	$-0.301493\pi$
$577$	673.918			1.16797			0.583985	+	0.811765i	$0.301493\pi$
$578$		0			0
$579$	−383.728	−	375.555i	−0.662743	−	0.648628i
$580$		0			0
$581$	1398.43	−	807.384i	2.40694	−	1.38965i
$582$		0			0
$583$	−32.3732	+	56.0720i	−0.0555286	+	0.0961784i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	337.196	+	194.680i	0.574439	+	0.331653i	0.758920	−	0.651183i	$-0.225727\pi$
$587$	337.196	+	194.680i	0.574439	+	0.331653i	−0.184481	+	0.982836i	$0.559061\pi$
$588$		0			0
$589$	24.0043	+	41.5766i	0.0407543	+	0.0705885i
$590$		0			0
$591$	−110.542	−	395.473i	−0.187043	−	0.669160i
$592$		0			0
$593$			640.797i			1.08060i	0.841472	+	0.540301i	$0.181690\pi$
$593$			640.797i			1.08060i	−0.841472	+	0.540301i	$0.818310\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−33.1206	+	9.25784i	−0.0554785	+	0.0155073i
$598$		0			0
$599$	−403.936	+	233.212i	−0.674350	+	0.389336i	−0.797723	−	0.603024i	$-0.793962\pi$
$599$	−403.936	+	233.212i	−0.674350	+	0.389336i	0.123373	+	0.992360i	$0.460629\pi$
$600$		0			0
$601$	493.215	−	854.273i	0.820657	−	1.42142i	−0.0845364	−	0.996420i	$-0.526941\pi$
$601$	493.215	−	854.273i	0.820657	−	1.42142i	0.905194	−	0.425000i	$-0.139726\pi$
$602$		0			0
$603$	528.518	+	290.155i	0.876482	+	0.481185i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−434.982	−	753.411i	−0.716610	−	1.24120i	−0.962335	−	0.271865i	$-0.912359\pi$
$607$	−434.982	−	753.411i	−0.716610	−	1.24120i	0.245725	−	0.969339i	$-0.420974\pi$
$608$		0			0
$609$	1029.79	−	1052.20i	1.69096	−	1.72776i
$610$		0			0
$611$			77.1267i			0.126230i
$612$		0			0
$613$	−376.400			−0.614029			−0.307014	−	0.951705i	$-0.599330\pi$
$613$	−376.400			−0.614029			−0.307014	+	0.951705i	$0.599330\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	100.567	−	58.0623i	0.162993	−	0.0941041i	−0.416285	−	0.909234i	$-0.636668\pi$
$617$	100.567	−	58.0623i	0.162993	−	0.0941041i	0.579278	+	0.815130i	$0.303335\pi$
$618$		0			0
$619$	119.765	−	207.439i	0.193482	−	0.335120i	−0.752920	−	0.658112i	$-0.771355\pi$
$619$	119.765	−	207.439i	0.193482	−	0.335120i	0.946402	+	0.322992i	$0.104689\pi$
$620$		0			0
$621$	4.89630	−	20.9578i	0.00788455	−	0.0337485i
$622$		0			0
$623$	−515.566	−	297.662i	−0.827553	−	0.477788i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	442.195	+	113.399i	0.705255	+	0.180860i
$628$		0			0
$629$			1030.78i			1.63877i
$630$		0			0
$631$	−590.863			−0.936392			−0.468196	−	0.883625i	$-0.655096\pi$
$631$	−590.863			−0.936392			−0.468196	+	0.883625i	$0.655096\pi$
$632$		0			0
$633$	166.046	+	162.509i	0.262315	+	0.256729i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	65.8715	−	114.093i	0.103409	−	0.179109i
$638$		0			0
$639$	−329.732	−	543.738i	−0.516013	−	0.850920i
$640$		0			0
$641$	663.399	+	383.014i	1.03494	+	0.597525i	0.918397	−	0.395660i	$-0.129484\pi$
$641$	663.399	+	383.014i	1.03494	+	0.597525i	0.116547	+	0.993185i	$0.462817\pi$
$642$		0			0
$643$	38.0263	+	65.8635i	0.0591389	+	0.102432i	0.894079	−	0.447909i	$-0.147831\pi$
$643$	38.0263	+	65.8635i	0.0591389	+	0.102432i	−0.834940	+	0.550341i	$0.814498\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	287.130i		−	0.443786i	−0.975071	−	0.221893i	$-0.928776\pi$
$647$		−	287.130i		−	0.443786i	0.975071	−	0.221893i	$-0.0712236\pi$
$648$		0			0
$649$	−268.545			−0.413783
$650$		0			0
$651$	−52.2383	+	14.6016i	−0.0802432	+	0.0224295i
$652$		0			0
$653$	−194.364	+	112.216i	−0.297647	+	0.171847i	−0.641386	−	0.767219i	$-0.721640\pi$
$653$	−194.364	+	112.216i	−0.297647	+	0.171847i	0.343738	+	0.939066i	$0.388307\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	178.151	−	108.034i	0.271158	−	0.164435i
$658$		0			0
$659$	942.931	+	544.401i	1.43085	+	0.826102i	0.997186	−	0.0749720i	$-0.0238867\pi$
$659$	942.931	+	544.401i	1.43085	+	0.826102i	0.433665	+	0.901074i	$0.357220\pi$
$660$		0			0
$661$	−439.376	−	761.021i	−0.664714	−	1.15132i	−0.979363	−	0.202110i	$-0.935220\pi$
$661$	−439.376	−	761.021i	−0.664714	−	1.15132i	0.314649	−	0.949208i	$-0.398113\pi$
$662$		0			0
$663$	60.7481	−	62.0701i	0.0916262	−	0.0936201i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	31.5986			0.0473743
$668$		0			0
$669$	−107.487	+	419.142i	−0.160669	+	0.626521i
$670$		0			0
$671$	−220.688	+	127.414i	−0.328894	+	0.189887i
$672$		0			0
$673$	278.142	−	481.757i	0.413287	−	0.715835i	−0.581960	−	0.813218i	$-0.697714\pi$
$673$	278.142	−	481.757i	0.413287	−	0.715835i	0.995247	+	0.0973831i	$0.0310472\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	486.720	+	281.008i	0.718937	+	0.415078i	0.814361	−	0.580358i	$-0.197087\pi$
$677$	486.720	+	281.008i	0.718937	+	0.415078i	−0.0954244	+	0.995437i	$0.530421\pi$
$678$		0			0
$679$	−119.938	−	207.739i	−0.176640	−	0.305949i
$680$		0			0
$681$	−142.693	−	36.5930i	−0.209534	−	0.0537342i
$682$		0			0
$683$		−	500.931i		−	0.733427i	−0.930334	−	0.366714i	$-0.880483\pi$
$683$		−	500.931i		−	0.733427i	0.930334	−	0.366714i	$-0.119517\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−216.505	−	211.894i	−0.315145	−	0.308433i
$688$		0			0
$689$	15.3054	−	8.83658i	0.0222139	−	0.0128252i
$690$		0			0
$691$	−361.250	+	625.703i	−0.522793	+	0.905504i	0.476855	+	0.878982i	$0.341777\pi$
$691$	−361.250	+	625.703i	−0.522793	+	0.905504i	−0.999648	+	0.0265221i	$0.991557\pi$
$692$		0			0
$693$	−248.208	+	452.112i	−0.358165	+	0.652399i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	448.330	+	776.530i	0.643228	+	1.11410i
$698$		0			0
$699$	−97.2883	−	348.056i	−0.139182	−	0.497934i
$700$		0			0
$701$		−	788.759i		−	1.12519i	−0.826732	−	0.562595i	$-0.809803\pi$
$701$		−	788.759i		−	1.12519i	0.826732	−	0.562595i	$-0.190197\pi$
$702$		0			0
$703$	1478.90			2.10370
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1388.44	+	801.618i	−1.96385	+	1.13383i
$708$		0			0
$709$	−199.643	+	345.792i	−0.281584	+	0.487718i	−0.971775	−	0.235910i	$-0.924193\pi$
$709$	−199.643	+	345.792i	−0.281584	+	0.487718i	0.690191	+	0.723627i	$0.257526\pi$
$710$		0			0
$711$	5.64602	+	262.245i	0.00794095	+	0.368839i
$712$		0			0
$713$	−1.00817	−	0.582067i	−0.00141398	−	0.000816364i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−380.635	+	388.918i	−0.530871	+	0.542424i
$718$		0			0
$719$			844.389i			1.17439i	0.809444	+	0.587197i	$0.199768\pi$
$719$			844.389i			1.17439i	−0.809444	+	0.587197i	$0.800232\pi$
$720$		0			0
$721$	−104.023			−0.144276
$722$		0			0
$723$	−120.955	+	471.660i	−0.167297	+	0.652365i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−202.857	+	351.359i	−0.279033	+	0.483300i	−0.971145	−	0.238491i	$-0.923347\pi$
$727$	−202.857	+	351.359i	−0.279033	+	0.483300i	0.692111	+	0.721791i	$0.256681\pi$
$728$		0			0
$729$	−47.0452	−	727.480i	−0.0645339	−	0.997916i
$730$		0			0
$731$	721.905	+	416.792i	0.987559	+	0.570167i
$732$		0			0
$733$	−602.495	−	1043.55i	−0.821958	−	1.42367i	−0.904222	−	0.427063i	$-0.859548\pi$
$733$	−602.495	−	1043.55i	−0.821958	−	1.42367i	0.0822636	−	0.996611i	$-0.473785\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	310.105i		−	0.420766i
$738$		0			0
$739$	−539.145			−0.729561			−0.364780	−	0.931094i	$-0.618856\pi$
$739$	−539.145			−0.729561			−0.364780	+	0.931094i	$0.618856\pi$
$740$		0			0
$741$	−89.0539	−	87.1572i	−0.120181	−	0.117621i
$742$		0			0
$743$	−269.337	+	155.502i	−0.362500	+	0.209289i	−0.670177	−	0.742202i	$-0.733782\pi$
$743$	−269.337	+	155.502i	−0.362500	+	0.209289i	0.307677	+	0.951491i	$0.400448\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1173.62	−	25.2676i	1.57112	−	0.0338255i
$748$		0			0
$749$	−655.497	−	378.452i	−0.875163	−	0.505276i
$750$		0			0
$751$	−463.288	−	802.439i	−0.616895	−	1.06849i	−0.990049	−	0.140724i	$-0.955057\pi$
$751$	−463.288	−	802.439i	−0.616895	−	1.06849i	0.373153	−	0.927770i	$-0.378276\pi$
$752$		0			0
$753$	359.751	+	1287.04i	0.477757	+	1.70921i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	450.364			0.594933			0.297467	−	0.954732i	$-0.403858\pi$
$757$	450.364			0.594933			0.297467	+	0.954732i	$0.403858\pi$
$758$		0			0
$759$	−10.6609	+	2.97992i	−0.0140460	+	0.00392612i
$760$		0			0
$761$	−581.319	+	335.624i	−0.763888	+	0.441031i	−0.830690	−	0.556735i	$-0.812054\pi$
$761$	−581.319	+	335.624i	−0.763888	+	0.441031i	0.0668021	+	0.997766i	$0.478720\pi$
$762$		0			0
$763$	1001.37	−	1734.42i	1.31241	−	2.27316i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	63.4815	+	36.6510i	0.0827659	+	0.0477849i
$768$		0			0
$769$	−37.3520	−	64.6955i	−0.0485721	−	0.0841294i	0.840717	−	0.541475i	$-0.182134\pi$
$769$	−37.3520	−	64.6955i	−0.0485721	−	0.0841294i	−0.889289	+	0.457345i	$0.848800\pi$
$770$		0			0
$771$	519.172	−	530.470i	0.673375	−	0.688028i
$772$		0			0
$773$		−	1226.34i		−	1.58647i	−0.608917	−	0.793234i	$-0.708396\pi$
$773$		−	1226.34i		−	1.58647i	0.608917	−	0.793234i	$-0.291604\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−415.060	+	1618.51i	−0.534182	+	2.08302i
$778$		0			0
$779$	1114.11	−	643.233i	1.43018	−	0.825716i
$780$		0			0
$781$	−163.533	+	283.247i	−0.209389	+	0.362673i
$782$		0			0
$783$	1024.36	−	310.249i	1.30825	−	0.396231i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−129.596	−	224.466i	−0.164670	−	0.285218i	0.771868	−	0.635783i	$-0.219323\pi$
$787$	−129.596	−	224.466i	−0.164670	−	0.285218i	−0.936538	+	0.350566i	$0.885989\pi$
$788$		0			0
$789$	249.984	+	64.1073i	0.316836	+	0.0812513i
$790$		0			0
$791$		−	423.986i		−	0.536013i
$792$		0			0
$793$	69.5579			0.0877149
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1286.14	+	742.554i	−1.61373	+	0.931686i	−0.625231	+	0.780439i	$0.714995\pi$
$797$	−1286.14	+	742.554i	−1.61373	+	0.931686i	−0.988496	+	0.151247i	$0.951671\pi$
$798$		0			0
$799$	699.290	−	1211.21i	0.875206	−	1.51590i
$800$		0			0
$801$	−224.410	−	370.059i	−0.280163	−	0.461996i
$802$		0			0
$803$	−92.8035	−	53.5801i	−0.115571	−	0.0667249i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	297.696	+	1065.03i	0.368893	+	1.31974i
$808$		0			0
$809$			10.2026i			0.0126114i	0.999980	+	0.00630569i	$0.00200718\pi$
$809$			10.2026i			0.0126114i	−0.999980	+	0.00630569i	$0.997993\pi$
$810$		0			0
$811$	1113.80			1.37337			0.686685	−	0.726955i	$-0.259065\pi$
$811$	1113.80			1.37337			0.686685	+	0.726955i	$0.259065\pi$
$812$		0			0
$813$	−377.739	+	105.585i	−0.464624	+	0.129871i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	597.985	−	1035.74i	0.731928	−	1.26774i
$818$		0			0
$819$	120.378	−	72.9995i	0.146982	−	0.0891324i
$820$		0			0
$821$	−266.290	−	153.742i	−0.324348	−	0.187262i	0.328981	−	0.944337i	$-0.393295\pi$
$821$	−266.290	−	153.742i	−0.324348	−	0.187262i	−0.653329	+	0.757074i	$0.726628\pi$
$822$		0			0
$823$	297.749	+	515.717i	0.361785	+	0.626630i	0.988255	−	0.152816i	$-0.0488340\pi$
$823$	297.749	+	515.717i	0.361785	+	0.626630i	−0.626469	+	0.779446i	$0.715501\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			1110.81i			1.34318i	0.740921	+	0.671592i	$0.234389\pi$
$827$			1110.81i			1.34318i	−0.740921	+	0.671592i	$0.765611\pi$
$828$		0			0
$829$	−390.454			−0.470994			−0.235497	−	0.971875i	$-0.575672\pi$
$829$	−390.454			−0.470994			−0.235497	+	0.971875i	$0.575672\pi$
$830$		0			0
$831$	161.915	−	631.381i	0.194844	−	0.759784i
$832$		0			0
$833$	−2068.90	+	1194.48i	−2.48368	+	1.43395i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−38.3976	−	8.97071i	−0.0458753	−	0.0107177i
$838$		0			0
$839$	−928.946	−	536.327i	−1.10721	−	0.639246i	−0.169102	−	0.985599i	$-0.554087\pi$
$839$	−928.946	−	536.327i	−1.10721	−	0.639246i	−0.938104	+	0.346353i	$0.887420\pi$
$840$		0			0
$841$	365.210	+	632.562i	0.434257	+	0.752155i
$842$		0			0
$843$	500.777	+	128.422i	0.594041	+	0.152340i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−1232.71			−1.45539
$848$		0			0
$849$	935.134	+	915.218i	1.10145	+	1.07800i
$850$		0			0
$851$	−31.0566	+	17.9305i	−0.0364942	+	0.0210700i
$852$		0			0
$853$	−454.724	+	787.604i	−0.533087	+	0.923334i	0.466166	+	0.884697i	$0.345635\pi$
$853$	−454.724	+	787.604i	−0.533087	+	0.923334i	−0.999253	+	0.0386371i	$0.987698\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−564.185	−	325.732i	−0.658325	−	0.380084i	0.133313	−	0.991074i	$-0.457438\pi$
$857$	−564.185	−	325.732i	−0.658325	−	0.380084i	−0.791639	+	0.610990i	$0.790772\pi$
$858$		0			0
$859$	230.239	+	398.786i	0.268032	+	0.464244i	0.968353	−	0.249583i	$-0.0802935\pi$
$859$	230.239	+	398.786i	0.268032	+	0.464244i	−0.700322	+	0.713827i	$0.746960\pi$
$860$		0			0
$861$	391.273	+	1399.81i	0.454441	+	1.62580i
$862$		0			0
$863$			359.492i			0.416560i	0.978069	+	0.208280i	$0.0667866\pi$
$863$			359.492i			0.416560i	−0.978069	+	0.208280i	$0.933213\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−681.776	+	190.569i	−0.786362	+	0.219803i
$868$		0			0
$869$	116.837	−	67.4560i	0.134450	−	0.0776249i
$870$		0			0
$871$	−42.3231	+	73.3057i	−0.0485914	+	0.0841627i
$872$		0			0
$873$	−3.75356	−	174.344i	−0.00429960	−	0.199707i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	569.520	+	986.437i	0.649395	+	1.12479i	0.983268	+	0.182167i	$0.0583112\pi$
$877$	569.520	+	986.437i	0.649395	+	1.12479i	−0.333872	+	0.942618i	$0.608355\pi$
$878$		0			0
$879$	−60.9379	+	62.2639i	−0.0693263	+	0.0708350i
$880$		0			0
$881$			1612.41i			1.83020i	0.403227	+	0.915100i	$0.367888\pi$
$881$			1612.41i			1.83020i	−0.403227	+	0.915100i	$0.632112\pi$
$882$		0			0
$883$	−688.542			−0.779775			−0.389888	−	0.920862i	$-0.627486\pi$
$883$	−688.542			−0.779775			−0.389888	+	0.920862i	$0.627486\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	974.792	−	562.797i	1.09898	−	0.634494i	0.163025	−	0.986622i	$-0.447875\pi$
$887$	974.792	−	562.797i	1.09898	−	0.634494i	0.935952	+	0.352128i	$0.114542\pi$
$888$		0			0
$889$	−645.747	+	1118.47i	−0.726374	+	1.25812i
$890$		0			0
$891$	−316.345	+	201.276i	−0.355045	+	0.225899i
$892$		0			0
$893$	−1737.75	−	1003.29i	−1.94597	−	1.12351i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	2.92683	+	0.750574i	0.00326291	+	0.000836761i
$898$		0			0
$899$		−	57.8931i		−	0.0643972i
$900$		0			0
$901$	−320.477			−0.355690
$902$		0			0
$903$	965.686	+	945.119i	1.06942	+	1.04664i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	311.993	−	540.388i	0.343984	−	0.595798i	−0.641185	−	0.767387i	$-0.721557\pi$
$907$	311.993	−	540.388i	0.343984	−	0.595798i	0.985169	+	0.171589i	$0.0548901\pi$
$908$		0			0
$909$	−1165.24	+	25.0872i	−1.28190	+	0.0275987i
$910$		0			0
$911$	−1321.03	−	762.700i	−1.45009	−	0.837212i	−0.451607	−	0.892217i	$-0.649149\pi$
$911$	−1321.03	−	762.700i	−1.45009	−	0.837212i	−0.998486	+	0.0550052i	$0.982482\pi$
$912$		0			0
$913$	−301.886	−	522.882i	−0.330653	−	0.572708i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	2719.09i		−	2.96520i
$918$		0			0
$919$	875.498			0.952663			0.476332	−	0.879266i	$-0.341966\pi$
$919$	875.498			0.952663			0.476332	+	0.879266i	$0.341966\pi$
$920$		0			0
$921$	−884.582	+	247.257i	−0.960458	+	0.268466i
$922$		0			0
$923$	77.3152	−	44.6379i	0.0837651	−	0.0483618i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−66.2894	−	36.3926i	−0.0715096	−	0.0392585i
$928$		0			0
$929$	−341.363	−	197.086i	−0.367452	−	0.212148i	0.304893	−	0.952387i	$-0.401379\pi$
$929$	−341.363	−	197.086i	−0.367452	−	0.212148i	−0.672345	+	0.740238i	$0.734713\pi$
$930$		0			0
$931$	1713.76	+	2968.32i	1.84077	+	3.18831i
$932$		0			0
$933$	−833.514	+	851.652i	−0.893370	+	0.912811i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−600.533			−0.640911			−0.320455	−	0.947264i	$-0.603836\pi$
$937$	−600.533			−0.640911			−0.320455	+	0.947264i	$0.603836\pi$
$938$		0			0
$939$	−291.950	+	1138.45i	−0.310916	+	1.21240i
$940$		0			0
$941$	−572.208	+	330.364i	−0.608085	+	0.351078i	−0.772216	−	0.635361i	$-0.780851\pi$
$941$	−572.208	+	330.364i	−0.608085	+	0.351078i	0.164131	+	0.986439i	$0.447518\pi$
$942$		0			0
$943$	−15.5974	+	27.0155i	−0.0165402	+	0.0286485i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1096.03	+	632.795i	1.15737	+	0.668210i	0.950673	−	0.310194i	$-0.100394\pi$
$947$	1096.03	+	632.795i	1.15737	+	0.668210i	0.206701	+	0.978404i	$0.433727\pi$
$948$		0			0
$949$	14.6252	+	25.3316i	0.0154112	+	0.0266930i
$950$		0			0
$951$	−470.150	−	120.568i	−0.494375	−	0.126780i
$952$		0			0
$953$			428.958i			0.450113i	0.974346	+	0.225057i	$0.0722567\pi$
$953$			428.958i			0.450113i	−0.974346	+	0.225057i	$0.927743\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−393.426	−	385.046i	−0.411103	−	0.402347i
$958$		0			0
$959$	2031.44	−	1172.85i	2.11829	−	1.22300i
$960$		0			0
$961$	479.434	−	830.403i	0.498890	−	0.864103i
$962$		0			0
$963$	−285.318	−	470.498i	−0.296281	−	0.488575i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−221.642	−	383.896i	−0.229206	−	0.396996i	0.728367	−	0.685187i	$-0.240280\pi$
$967$	−221.642	−	383.896i	−0.229206	−	0.396996i	−0.957573	+	0.288191i	$0.906946\pi$
$968$		0			0
$969$	608.277	+	2176.16i	0.627737	+	2.24578i
$970$		0			0
$971$			444.042i			0.457304i	0.973508	+	0.228652i	$0.0734317\pi$
$971$			444.042i			0.457304i	−0.973508	+	0.228652i	$0.926568\pi$
$972$		0			0
$973$	2724.11			2.79970
$974$		0			0
$975$		0			0
$976$		0			0
$977$	200.009	−	115.475i	0.204717	−	0.118194i	−0.394137	−	0.919052i	$-0.628956\pi$
$977$	200.009	−	115.475i	0.204717	−	0.118194i	0.598854	+	0.800858i	$0.295623\pi$
$978$		0			0
$979$	−111.298	+	192.773i	−0.113685	+	0.196908i
$980$		0			0
$981$	1244.92	−	754.940i	1.26903	−	0.769562i
$982$		0			0
$983$	971.023	+	560.620i	0.987816	+	0.570316i	0.904621	−	0.426218i	$-0.140154\pi$
$983$	971.023	+	560.620i	0.987816	+	0.570316i	0.0831949	+	0.996533i	$0.473488\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	1585.71	−	1620.22i	1.60660	−	1.64156i
$988$		0			0
$989$			29.0005i			0.0293230i
$990$		0			0
$991$	182.717			0.184377			0.0921884	−	0.995742i	$-0.470614\pi$
$991$	182.717			0.184377			0.0921884	+	0.995742i	$0.470614\pi$
$992$		0			0
$993$	−176.758	+	689.262i	−0.178005	+	0.694121i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	616.618	−	1068.01i	0.618473	−	1.07123i	−0.371291	−	0.928517i	$-0.621085\pi$
$997$	616.618	−	1068.01i	0.618473	−	1.07123i	0.989764	−	0.142711i	$-0.0455819\pi$
$998$		0			0
$999$	−830.737	+	886.195i	−0.831569	+	0.887082i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.p.f.101.12		24
3.2	odd	2		2700.3.p.f.1601.12		24
5.2	odd	4		180.3.t.a.29.6	✓	24
5.3	odd	4		180.3.t.a.29.7	yes	24
5.4	even	2	inner	900.3.p.f.101.1		24
9.4	even	3		2700.3.p.f.2501.12		24
9.5	odd	6	inner	900.3.p.f.401.12		24
15.2	even	4		540.3.t.a.89.5		24
15.8	even	4		540.3.t.a.89.10		24
15.14	odd	2		2700.3.p.f.1601.1		24
45.2	even	12		1620.3.b.b.809.22		24
45.4	even	6		2700.3.p.f.2501.1		24
45.7	odd	12		1620.3.b.b.809.3		24
45.13	odd	12		540.3.t.a.449.5		24
45.14	odd	6	inner	900.3.p.f.401.1		24
45.22	odd	12		540.3.t.a.449.10		24
45.23	even	12		180.3.t.a.149.6	yes	24
45.32	even	12		180.3.t.a.149.7	yes	24
45.38	even	12		1620.3.b.b.809.4		24
45.43	odd	12		1620.3.b.b.809.21		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.t.a.29.6	✓	24	5.2	odd	4
180.3.t.a.29.7	yes	24	5.3	odd	4
180.3.t.a.149.6	yes	24	45.23	even	12
180.3.t.a.149.7	yes	24	45.32	even	12
540.3.t.a.89.5		24	15.2	even	4
540.3.t.a.89.10		24	15.8	even	4
540.3.t.a.449.5		24	45.13	odd	12
540.3.t.a.449.10		24	45.22	odd	12
900.3.p.f.101.1		24	5.4	even	2	inner
900.3.p.f.101.12		24	1.1	even	1	trivial
900.3.p.f.401.1		24	45.14	odd	6	inner
900.3.p.f.401.12		24	9.5	odd	6	inner
1620.3.b.b.809.3		24	45.7	odd	12
1620.3.b.b.809.4		24	45.38	even	12
1620.3.b.b.809.21		24	45.43	odd	12
1620.3.b.b.809.22		24	45.2	even	12
2700.3.p.f.1601.1		24	15.14	odd	2
2700.3.p.f.1601.12		24	3.2	odd	2
2700.3.p.f.2501.1		24	45.4	even	6
2700.3.p.f.2501.12		24	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.88925 - 0.807601i) q^{3} +(6.19003 - 10.7214i) q^{7} +(7.69556 - 4.66673i) q^{9} +O(q^{10})\)	\(q+(2.88925 - 0.807601i) q^{3} +(6.19003 - 10.7214i) q^{7} +(7.69556 - 4.66673i) q^{9} +(-4.00882 - 2.31449i) q^{11} +(0.631764 + 1.09425i) q^{13} -22.9122i q^{17} -32.8729 q^{19} +(9.22592 - 35.9760i) q^{21} +(0.690324 - 0.398559i) q^{23} +(18.4656 - 19.6983i) q^{27} +(34.3302 + 19.8206i) q^{29} +(-0.730215 - 1.26477i) q^{31} +(-13.4517 - 3.44963i) q^{33} -44.9884 q^{37} +(2.70904 + 2.65134i) q^{39} +(-33.8915 + 19.5673i) q^{41} +(-18.1908 + 31.5074i) q^{43} +(52.8629 + 30.5204i) q^{47} +(-52.1330 - 90.2970i) q^{49} +(-18.5039 - 66.1992i) q^{51} -13.9872i q^{53} +(-94.9780 + 26.5482i) q^{57} +(50.2415 - 29.0069i) q^{59} +(27.5253 - 47.6752i) q^{61} +(-2.39828 - 111.395i) q^{63} +(33.4960 + 58.0167i) q^{67} +(1.67264 - 1.70904i) q^{69} -70.6560i q^{71} +23.1498 q^{73} +(-49.6294 + 28.6536i) q^{77} +(-14.5725 + 25.2404i) q^{79} +(37.4434 - 71.8261i) q^{81} +(112.958 + 65.2165i) q^{83} +(115.196 + 29.5415i) q^{87} -48.0873i q^{89} +15.6425 q^{91} +(-3.13120 - 3.06452i) q^{93} +(9.68803 - 16.7802i) q^{97} +(-41.6512 + 0.896733i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{9}+O(q^{10}) \) 24 * q - 2 * q^9	\( 24 q - 2 q^{9} - 18 q^{11} - 26 q^{21} - 36 q^{29} + 30 q^{31} - 6 q^{39} - 36 q^{41} - 108 q^{49} + 124 q^{51} + 306 q^{59} + 48 q^{61} + 268 q^{69} - 114 q^{79} - 14 q^{81} - 84 q^{91} - 418 q^{99}+O(q^{100}) \) 24 * q - 2 * q^9 - 18 * q^11 - 26 * q^21 - 36 * q^29 + 30 * q^31 - 6 * q^39 - 36 * q^41 - 108 * q^49 + 124 * q^51 + 306 * q^59 + 48 * q^61 + 268 * q^69 - 114 * q^79 - 14 * q^81 - 84 * q^91 - 418 * q^99

Introduction

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